A373558 Irregular triangle read by rows: T(1,1) = 1 and, for n >= 2, row n lists (in increasing order) the elements of the maximal Schreier set encoded by 2*A355489(n-1).
1, 2, 3, 2, 4, 2, 5, 3, 4, 5, 2, 6, 3, 4, 6, 3, 5, 6, 2, 7, 3, 4, 7, 3, 5, 7, 3, 6, 7, 4, 5, 6, 7, 2, 8, 3, 4, 8, 3, 5, 8, 3, 6, 8, 4, 5, 6, 8, 3, 7, 8, 4, 5, 7, 8, 4, 6, 7, 8, 2, 9, 3, 4, 9, 3, 5, 9, 3, 6, 9, 4, 5, 6, 9, 3, 7, 9, 4, 5, 7, 9, 4, 6, 7, 9, 3, 8, 9
Offset: 1
Examples
Triangle begins:
Corresponding
n 2*A355489(n-1) bin(2*A355489(n-1)) maximal Schreier set
(this sequence)
---------------------------------------------------------------
1 {1}
2 6 110 {2, 3}
3 10 1010 {2, 4}
4 18 10010 {2, 5}
5 28 11100 {3, 4, 4}
6 34 100010 {2, 6}
7 44 101100 {3, 4, 6}
8 52 110100 {3, 5, 6}
9 66 1000010 {2, 7}
10 76 1001100 {3, 4, 7}
11 84 1010100 {3, 5, 7}
12 100 1100100 {3, 6, 7}
13 120 1111000 {4, 5, 6, 7}
...
Links
- Paolo Xausa, Table of n, a(n) for n = 1..10003 (rows 1..1892 of the triangle, flattend).
- Alistair Bird, Jozef Schreier, Schreier sets and the Fibonacci sequence, Out Of The Norm blog, May 13 2012.
- Hùng Việt Chu, The Fibonacci Sequence and Schreier-Zeckendorf Sets, Journal of Integer Sequences, Vol. 22 (2019), Article 19.6.5.
Crossrefs
Programs
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Mathematica
Join[{{1}}, Map[PositionIndex[Reverse[IntegerDigits[#, 2]]][1] &, Select[Range[2, 500, 2], DigitCount[#, 2, 1] == IntegerExponent[#, 2] + 1 &]]]
Comments